The Yellowstone cutthroat trout population has decreased significantly in Yellowstone Lake in part due to increasing numbers of lake trout, which are not native to the park. The National Park Service has been removing lake trout in hopes that the population will collapse so the Yellowstone cutthroat trout can make a comeback. The catch rate is the number of lake trout that are caught per 100 meters of net per night. The numbers of lake trout removed and the catch rates are shown in Table 72 for various years.

Let n be the total number (in thousands) of lake trout removed and c be the catch rate (number of lake trout caught per 100 meters of net per night), both in the year that is x years since 2000.
a. Find a regression equation that models the association between x and n.
b. Find a regression equation that models the association between x and c.
c. Which of the two models is the better indicator of the number of lake trout that remain in the lake? Explain.
d. Compare the bases of the two models. What does your comparison mean in this situation? e. Use the catch-rate model to predict the catch rate in 2012. The actual catch rate was 6.7 lake trouts per 100 meters of net per night. Find the residual for your prediction.
f. On the basis of the comparison you made in part (d), explain why it is not surprising that the residual you found in part (e) is negative?

Transcribed Image Text:

Table 72 Numbers of Lake Trout Removed and Catch Rates Number of Lake Trout Removed (thousands) 16 24 Catch Rate (number of lake trout caught per 100 meters of net per night) 0.9 Year 1.8 1.9 37 76 79 102 148 2.6 4.7 4.8 4.9 8.2 2010 2011 2012 302